Description
The extensive additions, and the inclusion of a new chapter, has made this classic work by Jeffrey, now joined by co-author Dr. H.H. Dai, an even more essential reference for researchers and students in applied mathematics, engineering, and physics. It provides quick access to important formulas, relationships between functions, and mathematical techniques that range from matrix theory and integrals of commonly occurring functions to vector calculus, ordinary and partial differential equations, special functions, Fourier series, orthogonal polynomials, and Laplace and Fourier transforms. During the preparation of this edition full advantage was taken of the recently updated seventh edition of Gradshteyn and Ryzhik’s Table of Integrals, Series, and Products and other important reference works. Suggestions from users of the third edition of the Handbook have resulted in the expansion of many sections, and because of the relevance to boundary value problems for the Laplace equation in the plane, a new chapter on conformal mapping, has been added, complete with an atlas of useful mappings.
- Comprehensive coverage in reference form of the branches of mathematics used in science and engineering
- Organized to make results involving integrals and functions easy to locate
- Results illustrated by worked examples
Chapter
Index of Special Functions and Notations
pp.:
44 – 48
Chapter 0. Quick Reference List of Frequently Used Data
pp.:
48 – 74
Chapter 1. Numerical, Algebraic, and Analytical Results for Series and Calculus
pp.:
74 – 156
Chapter 2. Functions and Identities
pp.:
156 – 196
Chapter 3. Derivatives of Elementary Functions
pp.:
196 – 200
Chapter 4. Indefinite Integrals of Algebraic Functions
pp.:
200 – 222
Chapter 5. Indefinite Integrals of Exponential Functions
pp.:
222 – 228
Chapter 6. Indefinite Integrals of Logarithmic Functions
pp.:
228 – 236
Chapter 7. Indefinite Integrals of Hyperbolic Functions
pp.:
236 – 248
Chapter 8. Indefinite Integrals Involving Inverse Hyperbolic Functions
pp.:
248 – 254
Chapter 9. Indefinite Integrals of Trigonometric Functions
pp.:
254 – 272
Chapter 10. Indefinite Integrals of Inverse Trigonometric Functions
pp.:
272 – 278
Chapter 11. The Gamma, Beta, Pi, and Psi Functions, and the Incomplete Gamma Functions
pp.:
278 – 288
Chapter 12. Elliptic Integrals and Functions
pp.:
288 – 300
Chapter 13. Probability Distributions and Integrals, and the Error Function
pp.:
300 – 308
Chapter 14. Fresnel Integrals, Sine and Cosine Integrals
pp.:
308 – 312
Chapter 15. Definite Integrals
pp.:
312 – 322
Chapter 16. Different Forms of Fourier Series
pp.:
322 – 336
Chapter 17. Bessel Functions
pp.:
336 – 356
Chapter 18. Orthogonal Polynomials
pp.:
356 – 384
Chapter 19. Laplace Transformation
pp.:
384 – 400
Chapter 20. Fourier Transforms
pp.:
400 – 410
Chapter 21. Numerical Integration
pp.:
410 – 418
Chapter 22. Solutions of Standard Ordinary Differential Equations
pp.:
418 – 462
Chapter 23. Vector Analysis
pp.:
462 – 480
Chapter 24. Systems of Orthogonal Coordinates
pp.:
480 – 494
Chapter 25. Partial Differential Equations and Special Functions
pp.:
494 – 520
Chapter 26. Qualitative Properties of the Heat and Laplace Equation
pp.:
520 – 522
Chapter 27. Solutions of Elliptic, Parabolic, and Hyperbolic Equations
pp.:
522 – 540
Chapter 28. The z-Transform
pp.:
540 – 546
Chapter 29. Numerical Approximation
pp.:
546 – 556
Chapter 30. Conformal Mapping and Boundary Value Problems
pp.:
556 – 572
Short Classified Reference List
pp.:
572 – 576